Spin correlations in an interacting electron liquid are studied in the
high-frequency limit and in both two and three dimensions. The third-moment sum
rule is evaluated and used to derive exact limiting forms (at both long- and
short-wavelengths) for the spin-antisymmetric local-field factor, limω→∞G−(q,ω). In two dimensions limω→∞G−(q,ω) is found to diverge as 1/q at long wavelengths,
and the spin-antisymmetric exchange-correlation kernel of time-dependent spin
density functional theory diverges as 1/q2 in both two and three dimensions.
These signal a failure of the local-density approximation, one that can be
redressed by alternative approaches.Comment: 5 page